The word "plaza" is actually a Spanish word and had been adopted by major English dictionaries.

My issue is that I don't know how to correctly place the word in a store name. For example, if I want to use the word to name a store which sells bikes and bike accessories, should I name the store "Bike Plaza" or "Plaza Bike"?

I did some searches on Google and saw both usages. I hope to figure out the best usage.

It's a name. It can be anything you want. There can be no objective answer to this without more information about what your criteria are. Both versions of the store name are ambiguous and can be interpreted in multiple ways. (Which components are proper nouns and which common nouns?) Using a longer name would remove ambiguity. For example, Bikes in the Plaza, Plaza's Bikes, and The Bike Plaza.
– Jason BassfordSep 13 '18 at 15:41